which statement could be used in step 2 when proving x = 30

Of course! Im here to help!

Answer:

5x - y = - 3

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 5x + 3 ( subtract y from both sides )

0 = 5x - y + 3 ( subtract 3 from both sides )

- 3 = 5x - y, that is

5x - y = - 3 ← in standard form

Answer:

x-2y-8=0

Step-by-step explanation:

The equation of line is given by the relation

y-y1=m(x-x1)

where m is the slope

now, given x1=-4 and y1=-6 and the slope is 1/2.

substitute into the equation to get

y+6=1/2(x+4)

multiplying through with the L.C.M

which is 2

2(y+6)=1/2×2(x+4)

2y+12=x+4

making x the subject

x= 2y+8 hence the equation of the line is x-2y-8 =0

Final answer:

The equation of the line that passes through the point (-4, -6) with a slope of 1/2 is y = 1/2x - 4.

Explanation:

To find the equation of a line that passes through the point (-4, -6) with a slope of 1/2, we use the point-slope form of a line's equation which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point is (-4, -6) and the slope m is 1/2.

Plugging in the values, we get:

y - (-6) = (1/2)(x - (-4))

Simplify the equation:

y + 6 = 1/2x + 2

To get the equation in slope-intercept form y = mx + b, we do:

y = 1/2x + 2 - 6

y = 1/2x - 4

So the equation of the line is y = 1/2x - 4.

Answer:

462 sq in

Step-by-step explanation:

3((14 2/3)(10.5))

3(154)

462

A) Because the 80 is by itself that would be the start up fee.

B) We are told x is the number of months. Since the X is being multiplied by 30, we know that would be the total monthly cost. This is being added to the 80, which does not have an exponent, so we know this is a single cost, which would be the start up fee.

C) Copying the same format as the given equation above, change the numbers:

f(x) = 20 + 35x

D) I used the same format as the first equation, which meant replacing the start up cost from the original one ( 80) with the start up of the new one (20). Then I changed the monthly cost from the original one (30) with the monthly cost of the new one (35).

E) Replace x in each equation with 8 and calculate the cost of each:

80 + 30(8) = 80 + 240 = $320

20 + 35(8) = 20 + 280 = $300

The second club (club B) is the cheaper option for her.

Answer:

x = 10

Step-by-step explanation:

First you need to add like terms (x + x), which would give you 2x.

2x + 2 = 22

Then subtract 2 from both sides, causing it to cancel out one side, and 22 - 2, on the other side:

2x + 2 = 22

      -2     -2

22 - 2 is 20, giving you:

2x = 20

Then divide both sides by 2:

2x/2 = 20/2

And you should get x = 10 as your answer.

Answer: -4xy + 2x

Step-by-step explanation:

4xy - 8xy = -4xy

4x - 2x = 2x

Answer:

2x - 4xy    or     2x(1 - 2y)

Step-by-step explanation:

Simplify 4xy-2x+4x-8xy

We can start by rearranging the expression;

4xy-8xy -2x + 4x

Then we add or subtract numbers with the same variable

-4xy + 2x

We can further factorize the above since 2x is common between the two numbers, so we will factor out 2x

2x(-2y + 1)

This can be re-write as;

2x(1 - 2y)

Answer:

16

Step-by-step explanation:

The sum of 3 and 13 would look like this as an equation, 3 + 13 = ? Just add 3 to 13 and you get 16 as your answer.

Answer:

48 - 2x

Step-by-step explanation

minus = decreased

2x= twice a  number

The expression is 2n-48.

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

Let the number be n.

The expression formed form the sentence is

2n - 48

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Answer:

Option B. $72, because the price of each pack is $8

Step-by-step explanation:

Looking at the double number line we have that

The price of 2 packs of spaghetti is $16

The price of 4 packs of spaghetti is $32

The price of 6 packs of spaghetti is $48

The price of 8 packs of spaghetti is $64

To find out he units rate, divide the price by the number of packs

[tex]\$16/2=8\frac{\$}{pack}[/tex]

Find out what is the price of 9 packs of spaghetti

Multiply the unit rate by 9

[tex]8\frac{\$}{pack}(9\ packs)=\$72[/tex]

therefore

The price of 9 spaghetti packs is $72

Answer:

B. 72

Step-by-step explanation:

LOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOL

Answer:

8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

4[tex]\sqrt{2}[/tex] + 7[tex]\sqrt{2}[/tex] - 3[tex]\sqrt{2}[/tex]

Factor out [tex]\sqrt{2}[/tex] from each term

= [tex]\sqrt{2}[/tex](4 + 7 - 3) = 8[tex]\sqrt{2}[/tex]

Answer:

[tex]y>-3x+6[/tex]

Step-by-step explanation:

First find the equation of the "boundary line" that separates the two sections of the plane. It is very simple to find its slope_y-intercept form from the graph.

We can find the slope of the boundary line by examining the two points where it intersects the axes: It crosses the y-axis at (0,6) (0 for x, 6 units for y)

and also crosses the x axis at (2,0) (2 unites for x and 0 for y)

That means that from the y intersect crossing, in order to arrive at the x intersect crossing, one has to go:

2 units to the right (this is called "run")

and 6 units down (this is called "rise", but should be considered as a negative value because instead of "rising" is going down)

Therefore, the slope of the boundary line is: [tex]slope = \frac{rise}{run} = \frac{-6}{2} = -3[/tex]

We also see that the y-intercept is = 6 (the point at which the line crosses the y-axis.

Then, we can write the equation of the boundary line as:

[tex]y = -3 x + 6[/tex]

Now, the set of (x,y) points that are highlighted in the picture are those "ABOVE" the boundary line, that is those points where the y-value is greater than those defined by the boundary line. Since the boundary line is drawn with a dotted line, that indicates that those values corresponding to (x,y) values in the line itself should NOT be included.

We therefore arrive at an inequality that does not contain an equal sign (to preclude the actual (x,y) values in the line to be included). and which indicates that we want all the (x,y) points on the plane which have y-values greater than those define by the boundary line. That is:

[tex]y>-3x+6[/tex]

Answer:

Correct, as 4 is the only number repeating twice

Answer:

54 hundreds

Step-by-step explanation:

Answer: YES!

Step-by-step explanation:

IF you can divide it in 4 it is!

Answer:

No

Step-by-step explanation:

A perfect cube is something that is multiplied by itself 3 times.

For example, 8 is a perfect cube because 2×2×2 = 8

27 is a perfect cube because 3×3×3 = 27

64 is a perfect cube because 4×4×4 = 64

No number can be multiplied by itself three times to equal 48

Therefore its not a perfect square.

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Answer:

7/13

Step-by-step explanation:

more parts to the fraction

Answer:

[tex]\frac{7}{13}[/tex] > [tex]\frac{6}{13}[/tex]

Since both fractions have the same denominator, you can just compare through the numerator.

Hence, [tex]\frac{7}{13} > \frac{6}{13}[/tex]

The required value of the given expression would be fraction -9 17/72.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The expression is given in the question

⇒ (4 3/4) × 5/6 × ( -2 1/3)

We have to evaluate the given expression,

⇒ (4 3/4) × 5/6 × ( -2 1/3)

⇒ (4 3/4) × 5/6 × (-1)(2 1/3)

⇒ (4 + 3/4) × 5/6 × (-1)(2 + 1/3)

⇒ (19/4) × 5/6 × (-1)(7/3)

⇒ 85/24 × (-7/3)

Apply the multiplication operation,

⇒ -665/72

Apply the division operation,

⇒ -9.236111

⇒ -9 17/72

Therefore, the required value of the given expression would be fraction -9 17/72.

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Final answer:

The expression 4 3/4 * 5/6 * -2 1/3 evaluates to -665/72 after converting mixed numbers to improper fractions and then multiplying the numerators and denominators. The result is in its simplest form.

Explanation:

The question involves evaluating a mathematical expression with mixed numbers and fractions and writing the answer in its simplest form. To solve this, we first convert mixed numbers to improper fractions. The expression given is 4 3/4 * 5/6 * -2 1/3. First, convert the mixed numbers:

Now multiply the improper fractions:

Multiply the numerators: 19 * 5 * (-7) = -665
Multiply the denominators: 4 * 6 * 3 = 72
Therefore, the result is -665/72. This is already in its simplest form as the numerator and denominator have no common factors.

x + 300 = 450 is the correct answer. This is becuause the unknown amount, x, is how much she put in the bank. $450 is her total, so it would be equal to 450. If she already had 300, you need to firgure out what she added to 300 to make the answer 450, so the correct answer is x + 300 = 450.

Answer:

Her wage on the 8th day is $105 ⇒ answer d

Step-by-step explanation:

* Lets explain how to solve the problem

- The average of set of data = The sum of data/the number of data

- The sum of data = the average of set of data × the number of data

∵ Cindy worked for 15 consecutive days

∵ She is earning an average wage of $91 per day

∴ Her total earning = 91 × 15 = $1365

∵ Her average earning during the first 7 days is $87 per day

∴ Her total earning in the first 7 days = 87 × 7 = $609

∵ Her average earning during the last 7 days is $93 per day

∴ Her total earning in the last 7 days = 93 × 7 = $651

- Her total earning in the 14 days is the sum of the earning in the

 first 7 days and the earning during the last 7 days

∵ Her total earning in the 14 days = 609 + 651 = $1260

∵ Her total earning in the 15 days is $1365

- To find her wage on the 8th day subtract her wage of the 14 days

  from her wage of the 15 days

∴ Her wage on the 8th day = 1365 - 1260 = $105

* Her wage on the 8th day is $105

18x^4+72x^3 is the answer to your question

Answer: 9x^2(2x^2+8x)

2x^2 8x

9x^2. 18x^4 72x^3

18x^4 + 72x^3

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

6/(7/28)

6/(1/4)

6 * 4/1

6 * 4

24

Answer:

9

Step-by-step explanation:

Answer:

infinite solutions

Step-by-step explanation:

Given

- 6(n - 8) = 4(12 - 5n) + 14n ← distribute parenthesis on both sides

- 6n + 48 = 48 - 20n + 14n, that is

- 6n + 48 = 48 - 6n ( add 6n to both sides )

48 = 48 ← True

This indicates that the equation is true for any value of n

Answer:

This is a very classical type of equation in which, the solution is basically any number and it is known as an "Identity". So it has infinite solutions

Step-by-step explanation:

-6(n-8) = 4(12-5n)+14n

-6n-6*(-8) = 4*12+4*(-5n) + 14n

-6n+48=48-20n+14n

-6n+48=48-6n

-6n+48=48-6n

-6n +6n + 48 -48 = 48 -48 - 6n + 6n

0 = 0

Answer:

A

Step-by-step explanation:

In the expression

[tex]0.90(2.25d+1.40t+6),[/tex]

d is the number of drinks Lindy orders;

t is the number of toppings Lindy orders.

If Lindy and her friends order 4 drinks and a medium pizza with 3 toppings, then d = 4 and t = 3. Find the value of the expression above when d = 4 and t = 3:

[tex]0.90(2.25\cdot 4+1.40\cdot 3+6)=0.90(9+4.20+6)=0.90\cdot 19.20=17.28[/tex]

So, Lindy and her friends will pay $17.28

Lindy's total cost for ordering 4 drinks and a pizza with 3 toppings amounts to $17.28, so the correct answer is Option A.

First, we substitute the given number of drinks and toppings into the expression, resulting in 0.90(2.25*4 + 1.40*3 + 6). That simplifies to 0.90(9 + 4.2 + 6), which further simplifies to 0.90(19.2). Finally, we multiply 0.90 by 19.2 to get the total cost, that is $17.28, which implies the correct answer is Option A.

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Step-by-step explanation:

let the num be 3x & 4x

3x+4x=28

7x=28

x=28/7

x=4

now, num of girls=3x=3×4=12

& num of boys=4x=4×4=16

Answer: 12 girls

Step-by-step explanation: You first want to make this equation become a fraction with the number of girls on top and the total on bottom. This becomes 3/7. To make this over 28, multiply by 4 on the top and the bottom. This makes 12/28, making 12 girls the answer.

Answer:

The answer to your question is: -17°C

Step-by-step explanation:

Data

Initial temperature = 7°C at 3:00 pm

Temperature drops 6°C every hour

Temperature at 7:00 pm

Process             Temperature

3:00                          7°C

4:00         -6°C           1°C      

5:00         -6°C          -5°C

6:00         -6°C          -11°C

7:00          -6°C          -17°C

1.0730000000000000000000000000

I searched it up

Answer:

1. C

2. C

3. A

Step-by-step explanation: